Three cats kill a total of 3 rats in 180 seconds. How many minutes would it take for 100 cats to kill 100 rats?

\(\bold{\huge{\underline{ Solution}}}\)

Let assume that the distance between the golf ball and central of green is x

Here,

According to the law of cosine :-

\(\bold{\red{ a^{2} = b^{2} + c^{2} - 2ABcos}}{\bold{\red{\theta}}}\)

So, For Hypotenuse law of cosine will be :-

\(\sf{ c^{2} = a^{2} + b^{2} - 2ABcos}{\sf{\theta}}\)

Subsitute the required values,

\(\sf{ x^{2} = (150)^{2} + (30)^{2} - 2(150)(30)cos}{\sf{100°}}\)

\(\sf{ x^{2} = 22500 + 900 - 900cos}{\sf{\times{\dfrac{5π}{9}}}}\)

\(\sf{ x^{2} = 22500 + 900 - 900( - 0.174)}\)

\(\sf{ x^{2} = 22500 + 900 + 156.6}\)

\(\sf{ x^{2} = 23556.6}\)

\(\bold{ x = 153.48\: yards }\)

Hence, The distance between the ball and the center of green is 153.48 or 153.5 yards

The value of the expression 7+[9÷(9x1 to the second power)] is 64/9

A fraction can be described as the part of a whole set or element.

There are several types of fractions, which includes;

Some examples of these fractions are given as;

Simple fractions: 1/5, 1/6

Mixed fractions: 2 1/8, 3 1/4

Proper fractions: 2/3, 4/5

Improper fractions; 4/1, 6/3

Given the expression;

7+[9÷(9x1 to the second power)]

This is expressed as;

7 + ( 9 ÷ (9)^2

Find the square

7 + ( 9 ÷ 81)

find the ratio

7 + 1/9

Find the common multiple

63 + 1 /9

64/9

Hence, the value is 64/9

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9514 1404 393

Answer:

  $7

Step-by-step explanation:

Let r and g represent the costs of a rose bush and a geranium, respectively. The given relations are ...

  14r +12g = 206

  g = 2r -5

Using the second equation to substitute for g in the first equation, we have ...

  14r +12(2r -5) = 206

  38r -60 = 206

  38r = 266

  r = 266/38 = 7

The cost of one rose bush is $7.

Answer:

?????????

Step-by-step explanation:

Answer:

a)  \(Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}\)

b)  \(n=24\)

Step-by-step explanation:

From the question we are told that:

Rate r=90 units per hour

Setup cost =20

Operating Cost =26

Units=40000

Generally the equation for Total cost is mathematically given by

\(Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}\)

\(T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1\)

Differentiating

\(T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2\)

Equating equ 1 to zero

\(0=\frac{20n^2+11556}{n}\)

\(n=24\)

Therefore

Substituting n

For Equ 1

\(T_n=\frac{20(24)^2+11556}{24}\)

F(n)>0  

For Equ 2

\(T_n'=\frac{20(24)^2-11556}{24^2}\)

F(n)'<0

4/15 = 3.75

10/13 = 1.3    

you have to divide it from its higher number or you'll get something like this: 0.7692307692307692 but if it helps it = 0.00205128205

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Look up "Everything You Need To Know About Math In One Big Fat Notebook pdf." It's the best thing I've ever been given, I have it with me in math class all the time and I've aced every test. I have it with me right now and it has everything I've ever been taught about math in it so it might help you.

The algebraic expression for the sentence in this problem is given as follows:

n - (x + 8).

The sentence in this problem is given as follows:

"A number n minus the sum of the number and eight".

The sum of an unknown number x and eight is given as follows:

x + 8.

The subtraction of the number n by the expression is given as follows:

n - (x + 8).

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The scaling shown in the attachment is about as close as I can get using an on-line graphing program. You may fare better with graph paper. The vertex and x-intercepts are shown. The values at x=-3 and x=2 are y=11.

If you have any specific questions or need assistance, feel free to ask, and I'll do my best to provide a helpful response within the scope of my training

As an AI language model my understanding of subjects and skills is based on the information and data available to me up until my last training update in September 2021. I can provide accurate and comprehensive responses within the limits of my training, but please keep in mind that I may not have knowledge of events or developments that have occurred after that cutoff date.

With a wide range of general knowledge, I can understand and generate responses on various topics such as science, history, literature, mathematics, and more. I can also assist with specific skills like writing, editing, brainstorming ideas, offering explanations, and providing recommendations.

However, it's important to note that while I strive to be helpful, I am still an AI and may not always provide perfect answers. I do not possess personal experiences or opinions, and I am not able to perform physical actions. My responses are generated based on patterns and examples from my training data.

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.

Answer:

Step-by-step explanation:

The answer is 4230

Answer:

49.98

Step-by-step explanation:

The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11

A composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.

The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.

i.e. the function g(x) = 11 always returns the value 11, regardless of the input.

Therefore, we have:

g(-3) = 11

g(5) = 11

g(a) = 11

g(a+h) = 11

So, regardless of the value of a or h, the function g(x) will always return 11.

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Answer:

2.192

Step-by-step explanation:

Answer: you would get 6 games and 2 books

Step-by-step explanation:

Answer:

-----------------------

Substitute 12 and 24 for n into formula and calculate.

So, the 12th term is 63 and 24th term is 123.

Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

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Answer:

x=6

Step-by-step explanation:

Rearrange terms:

8+x=14

x+8=14

Subtract 8 from both sides and simplify.

Given :-

To find :-

Solution :-

8+x = 14

x = 14-8 (Signs change when transferred to opposite side)

x = 6

Answer:

x = 4

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 14. Its slope is 0. A line perpendicular to this one will have a slope that is undefined, which is a vertical line.

Vertical lines have this equation: x = #

In this case, your x-value has to include 4.

Therefore, a line perpendicular to y = 14 that includes (4, -12) will have to be: x = 4.

Hope this helps!

Answer:

30

Step-by-step explanation:

8 times 3=24

3 times 2=6

24+6=30

The equation of the curve is given by:

Differentiating both sides of the equation with respect to x, we have:

Therefore, the slope of the tangent is given by the value of dy/dx when x= π / 2

Using the point slope formula, it follows that:

Therefore, the equation of the tangent at P is given by:

y = -x + π /2 + 3

Answer:

100%?

Step-by-step explanation:

Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

Answer:

Step-by-step explanation:

A + B = (-4x^2 +2x -5) +(3x^2 +6) = x^2(-4+3) +x(2) +(-5+6) = -x^2 +2x +1

  The given sum is Incorrect.

__

A - C = (-4x^2 +2x -5) -(-5x -4) = -4x^2 +x(2+5) +(-5+4) = -4x^2 +7x -1

   The given difference is Correct.

__

B + C = (3x^2 +6) +(-5x -4) = 3x^2 -6x +2

  The given sum is Incorrect.

Answer:

you shouldn't be cheating kid

Answer:

$16

Step-by-step explanation:

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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